Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A

Percentage Accurate: 85.7% → 99.6%

Time: 14.5s

Alternatives: 23

Speedup: 0.3×

Specification

Math

\[\begin{array}{l} \\ x + \frac{y \cdot \left(z - t\right)}{z - a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) (- z a))))

C

double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / (z - a));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y * (z - t)) / (z - a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / (z - a));
}

Python

def code(x, y, z, t, a):
	return x + ((y * (z - t)) / (z - a))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(z - a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + ((y * (z - t)) / (z - a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 85.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y \cdot \left(z - t\right)}{z - a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) (- z a))))

C

double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / (z - a));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y * (z - t)) / (z - a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / (z - a));
}

Python

def code(x, y, z, t, a):
	return x + ((y * (z - t)) / (z - a))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(z - a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + ((y * (z - t)) / (z - a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+278}:\\ \;\;\;\;y \cdot \left(\frac{z - t}{z - a} + \frac{x}{y}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (<= t_1 -5e+278)
     (* y (+ (/ (- z t) (- z a)) (/ x y)))
     (if (<= t_1 5e+304) (+ x t_1) (+ x (/ (- z t) (/ (- z a) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if (t_1 <= -5e+278) {
		tmp = y * (((z - t) / (z - a)) + (x / y));
	} else if (t_1 <= 5e+304) {
		tmp = x + t_1;
	} else {
		tmp = x + ((z - t) / ((z - a) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / (z - a)
    if (t_1 <= (-5d+278)) then
        tmp = y * (((z - t) / (z - a)) + (x / y))
    else if (t_1 <= 5d+304) then
        tmp = x + t_1
    else
        tmp = x + ((z - t) / ((z - a) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if (t_1 <= -5e+278) {
		tmp = y * (((z - t) / (z - a)) + (x / y));
	} else if (t_1 <= 5e+304) {
		tmp = x + t_1;
	} else {
		tmp = x + ((z - t) / ((z - a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if t_1 <= -5e+278:
		tmp = y * (((z - t) / (z - a)) + (x / y))
	elif t_1 <= 5e+304:
		tmp = x + t_1
	else:
		tmp = x + ((z - t) / ((z - a) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -5e+278)
		tmp = Float64(y * Float64(Float64(Float64(z - t) / Float64(z - a)) + Float64(x / y)));
	elseif (t_1 <= 5e+304)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(z - a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if (t_1 <= -5e+278)
		tmp = y * (((z - t) / (z - a)) + (x / y));
	elseif (t_1 <= 5e+304)
		tmp = x + t_1;
	else
		tmp = x + ((z - t) / ((z - a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+278], N[(y * N[(N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+304], N[(x + t$95$1), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -5.00000000000000029e278

   1. Initial program 44.3%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(\frac{x}{y} + \frac{z}{z - a}\right) - \frac{t}{z - a}\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 99.9%

         \[\leadsto y \cdot \color{blue}{\left(\frac{x}{y} + \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\right)} \]

      2. div-sub 99.9%

         \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\frac{z - t}{z - a}}\right) \]

   5. Simplified 99.9%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} + \frac{z - t}{z - a}\right)} \]

   if -5.00000000000000029e278 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 4.9999999999999997e304

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   if 4.9999999999999997e304 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 38.6%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 38.5%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. inv-pow 38.5%

         \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]

   4. Applied egg-rr 38.5%

      \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 38.5%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. associate-/r* 99.7%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{z - a}{y}}{z - t}}} \]

   6. Simplified 99.7%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{z - a}{y}}{z - t}}} \]
   7. Step-by-step derivation

      1. clear-num 99.9%

         \[\leadsto x + \color{blue}{\frac{z - t}{\frac{z - a}{y}}} \]

      2. add-cube-cbrt 99.0%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}}{\frac{z - a}{y}} \]

      3. div-inv 98.9%

         \[\leadsto x + \frac{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}{\color{blue}{\left(z - a\right) \cdot \frac{1}{y}}} \]

      4. times-frac 71.1%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{z - a} \cdot \frac{\sqrt[3]{z - t}}{\frac{1}{y}}} \]

      5. pow2 71.1%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{z - t}\right)}^{2}}}{z - a} \cdot \frac{\sqrt[3]{z - t}}{\frac{1}{y}} \]

   8. Applied egg-rr 71.1%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2}}{z - a} \cdot \frac{\sqrt[3]{z - t}}{\frac{1}{y}}} \]
   9. Step-by-step derivation

      1. times-frac 98.9%

         \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2} \cdot \sqrt[3]{z - t}}{\left(z - a\right) \cdot \frac{1}{y}}} \]

      2. unpow2 98.9%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)} \cdot \sqrt[3]{z - t}}{\left(z - a\right) \cdot \frac{1}{y}} \]

      3. rem-3cbrt-lft 99.7%

         \[\leadsto x + \frac{\color{blue}{z - t}}{\left(z - a\right) \cdot \frac{1}{y}} \]

      4. associate-*r/ 99.9%

         \[\leadsto x + \frac{z - t}{\color{blue}{\frac{\left(z - a\right) \cdot 1}{y}}} \]

      5. *-rgt-identity 99.9%

         \[\leadsto x + \frac{z - t}{\frac{\color{blue}{z - a}}{y}} \]

   10. Simplified 99.9%

       \[\leadsto x + \color{blue}{\frac{z - t}{\frac{z - a}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -5 \cdot 10^{+278}:\\ \;\;\;\;y \cdot \left(\frac{z - t}{z - a} + \frac{x}{y}\right)\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (fma y (/ (- z t) (- z a)) x))

C

double code(double x, double y, double z, double t, double a) {
	return fma(y, ((z - t) / (z - a)), x);
}

Julia

function code(x, y, z, t, a)
	return fma(y, Float64(Float64(z - t) / Float64(z - a)), x)
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 83.7%

   \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
2. Step-by-step derivation

   1. +-commutative 83.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{z - a} + x} \]

   2. associate-/l* 98.4%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{z - a}} + x \]

   3. fma-define 98.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]

3. Simplified 98.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
4. Add Preprocessing

5. Final simplification 98.4%

   \[\leadsto \mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right) \]
6. Add Preprocessing

Alternative 3: 72.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot \left(z - t\right)}{z}\\ t_2 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+129}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-189}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+66}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+130}:\\ \;\;\;\;x + \frac{1}{\frac{1}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y (- z t)) z))) (t_2 (* y (/ (- z t) (- z a)))))
   (if (<= y -7.5e+129)
     t_2
     (if (<= y -1.15e-71)
       t_1
       (if (<= y 1.16e-189)
         (+ y x)
         (if (<= y 7e-11)
           t_1
           (if (<= y 4.5e+66)
             (* (- z t) (/ y (- z a)))
             (if (<= y 1.7e+130) (+ x (/ 1.0 (/ 1.0 y))) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * (z - t)) / z);
	double t_2 = y * ((z - t) / (z - a));
	double tmp;
	if (y <= -7.5e+129) {
		tmp = t_2;
	} else if (y <= -1.15e-71) {
		tmp = t_1;
	} else if (y <= 1.16e-189) {
		tmp = y + x;
	} else if (y <= 7e-11) {
		tmp = t_1;
	} else if (y <= 4.5e+66) {
		tmp = (z - t) * (y / (z - a));
	} else if (y <= 1.7e+130) {
		tmp = x + (1.0 / (1.0 / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y * (z - t)) / z)
    t_2 = y * ((z - t) / (z - a))
    if (y <= (-7.5d+129)) then
        tmp = t_2
    else if (y <= (-1.15d-71)) then
        tmp = t_1
    else if (y <= 1.16d-189) then
        tmp = y + x
    else if (y <= 7d-11) then
        tmp = t_1
    else if (y <= 4.5d+66) then
        tmp = (z - t) * (y / (z - a))
    else if (y <= 1.7d+130) then
        tmp = x + (1.0d0 / (1.0d0 / y))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * (z - t)) / z);
	double t_2 = y * ((z - t) / (z - a));
	double tmp;
	if (y <= -7.5e+129) {
		tmp = t_2;
	} else if (y <= -1.15e-71) {
		tmp = t_1;
	} else if (y <= 1.16e-189) {
		tmp = y + x;
	} else if (y <= 7e-11) {
		tmp = t_1;
	} else if (y <= 4.5e+66) {
		tmp = (z - t) * (y / (z - a));
	} else if (y <= 1.7e+130) {
		tmp = x + (1.0 / (1.0 / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * (z - t)) / z)
	t_2 = y * ((z - t) / (z - a))
	tmp = 0
	if y <= -7.5e+129:
		tmp = t_2
	elif y <= -1.15e-71:
		tmp = t_1
	elif y <= 1.16e-189:
		tmp = y + x
	elif y <= 7e-11:
		tmp = t_1
	elif y <= 4.5e+66:
		tmp = (z - t) * (y / (z - a))
	elif y <= 1.7e+130:
		tmp = x + (1.0 / (1.0 / y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * Float64(z - t)) / z))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(z - a)))
	tmp = 0.0
	if (y <= -7.5e+129)
		tmp = t_2;
	elseif (y <= -1.15e-71)
		tmp = t_1;
	elseif (y <= 1.16e-189)
		tmp = Float64(y + x);
	elseif (y <= 7e-11)
		tmp = t_1;
	elseif (y <= 4.5e+66)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	elseif (y <= 1.7e+130)
		tmp = Float64(x + Float64(1.0 / Float64(1.0 / y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * (z - t)) / z);
	t_2 = y * ((z - t) / (z - a));
	tmp = 0.0;
	if (y <= -7.5e+129)
		tmp = t_2;
	elseif (y <= -1.15e-71)
		tmp = t_1;
	elseif (y <= 1.16e-189)
		tmp = y + x;
	elseif (y <= 7e-11)
		tmp = t_1;
	elseif (y <= 4.5e+66)
		tmp = (z - t) * (y / (z - a));
	elseif (y <= 1.7e+130)
		tmp = x + (1.0 / (1.0 / y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e+129], t$95$2, If[LessEqual[y, -1.15e-71], t$95$1, If[LessEqual[y, 1.16e-189], N[(y + x), $MachinePrecision], If[LessEqual[y, 7e-11], t$95$1, If[LessEqual[y, 4.5e+66], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+130], N[(x + N[(1.0 / N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.4999999999999998e129 or 1.7e130 < y

   1. Initial program 59.3%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.6%

      \[\leadsto \color{blue}{y \cdot \left(\left(\frac{x}{y} + \frac{z}{z - a}\right) - \frac{t}{z - a}\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 99.6%

         \[\leadsto y \cdot \color{blue}{\left(\frac{x}{y} + \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\right)} \]

      2. div-sub 99.6%

         \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\frac{z - t}{z - a}}\right) \]

   5. Simplified 99.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} + \frac{z - t}{z - a}\right)} \]

   6. Taylor expanded in x around 0 86.5%

      \[\leadsto y \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{t}{z - a}\right)} \]
   7. Step-by-step derivation

      1. div-sub 86.5%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{z - a}} \]

   8. Simplified 86.5%

      \[\leadsto y \cdot \color{blue}{\frac{z - t}{z - a}} \]

   if -7.4999999999999998e129 < y < -1.1499999999999999e-71 or 1.1600000000000001e-189 < y < 7.00000000000000038e-11

   1. Initial program 99.8%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 80.2%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{z}} \]

   if -1.1499999999999999e-71 < y < 1.1600000000000001e-189

   1. Initial program 100.0%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 90.9%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 90.9%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 90.9%

      \[\leadsto \color{blue}{y + x} \]

   if 7.00000000000000038e-11 < y < 4.4999999999999998e66

   1. Initial program 94.8%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 71.8%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{z - a}} \]
   4. Step-by-step derivation

      1. associate-*l/ 76.9%

         \[\leadsto \color{blue}{\frac{y}{z - a} \cdot \left(z - t\right)} \]

   5. Simplified 76.9%

      \[\leadsto \color{blue}{\frac{y}{z - a} \cdot \left(z - t\right)} \]

   if 4.4999999999999998e66 < y < 1.7e130

   1. Initial program 63.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 63.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. inv-pow 63.1%

         \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]

   4. Applied egg-rr 63.1%

      \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 63.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. associate-/r* 99.8%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{z - a}{y}}{z - t}}} \]

   6. Simplified 99.8%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{z - a}{y}}{z - t}}} \]

   7. Taylor expanded in z around inf 75.4%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-71}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-189}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+66}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+130}:\\ \;\;\;\;x + \frac{1}{\frac{1}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+304}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+304)))
     (+ x (/ (- z t) (/ (- z a) y)))
     (+ x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+304)) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+304)) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+304):
		tmp = x + ((z - t) / ((z - a) / y))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+304))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(z - a) / y)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+304)))
		tmp = x + ((z - t) / ((z - a) / y));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+304]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 4.9999999999999997e304 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 39.2%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 39.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. inv-pow 39.1%

         \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]

   4. Applied egg-rr 39.1%

      \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 39.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. associate-/r* 99.8%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{z - a}{y}}{z - t}}} \]

   6. Simplified 99.8%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{z - a}{y}}{z - t}}} \]
   7. Step-by-step derivation

      1. clear-num 99.9%

         \[\leadsto x + \color{blue}{\frac{z - t}{\frac{z - a}{y}}} \]

      2. add-cube-cbrt 98.9%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}}{\frac{z - a}{y}} \]

      3. div-inv 98.9%

         \[\leadsto x + \frac{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}{\color{blue}{\left(z - a\right) \cdot \frac{1}{y}}} \]

      4. times-frac 73.7%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{z - a} \cdot \frac{\sqrt[3]{z - t}}{\frac{1}{y}}} \]

      5. pow2 73.7%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{z - t}\right)}^{2}}}{z - a} \cdot \frac{\sqrt[3]{z - t}}{\frac{1}{y}} \]

   8. Applied egg-rr 73.7%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2}}{z - a} \cdot \frac{\sqrt[3]{z - t}}{\frac{1}{y}}} \]
   9. Step-by-step derivation

      1. times-frac 98.9%

         \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2} \cdot \sqrt[3]{z - t}}{\left(z - a\right) \cdot \frac{1}{y}}} \]

      2. unpow2 98.9%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)} \cdot \sqrt[3]{z - t}}{\left(z - a\right) \cdot \frac{1}{y}} \]

      3. rem-3cbrt-lft 99.7%

         \[\leadsto x + \frac{\color{blue}{z - t}}{\left(z - a\right) \cdot \frac{1}{y}} \]

      4. associate-*r/ 99.9%

         \[\leadsto x + \frac{z - t}{\color{blue}{\frac{\left(z - a\right) \cdot 1}{y}}} \]

      5. *-rgt-identity 99.9%

         \[\leadsto x + \frac{z - t}{\frac{\color{blue}{z - a}}{y}} \]

   10. Simplified 99.9%

       \[\leadsto x + \color{blue}{\frac{z - t}{\frac{z - a}{y}}} \]

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 4.9999999999999997e304

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 5 \cdot 10^{+304}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+278}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;t\_1 \leq 10^{+307}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (<= t_1 -5e+278)
     (* y (/ (- z t) (- z a)))
     (if (<= t_1 1e+307) (+ x t_1) (* (- z t) (/ y (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if (t_1 <= -5e+278) {
		tmp = y * ((z - t) / (z - a));
	} else if (t_1 <= 1e+307) {
		tmp = x + t_1;
	} else {
		tmp = (z - t) * (y / (z - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / (z - a)
    if (t_1 <= (-5d+278)) then
        tmp = y * ((z - t) / (z - a))
    else if (t_1 <= 1d+307) then
        tmp = x + t_1
    else
        tmp = (z - t) * (y / (z - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if (t_1 <= -5e+278) {
		tmp = y * ((z - t) / (z - a));
	} else if (t_1 <= 1e+307) {
		tmp = x + t_1;
	} else {
		tmp = (z - t) * (y / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if t_1 <= -5e+278:
		tmp = y * ((z - t) / (z - a))
	elif t_1 <= 1e+307:
		tmp = x + t_1
	else:
		tmp = (z - t) * (y / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -5e+278)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(z - a)));
	elseif (t_1 <= 1e+307)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if (t_1 <= -5e+278)
		tmp = y * ((z - t) / (z - a));
	elseif (t_1 <= 1e+307)
		tmp = x + t_1;
	else
		tmp = (z - t) * (y / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+278], N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+307], N[(x + t$95$1), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -5.00000000000000029e278

   1. Initial program 44.3%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(\frac{x}{y} + \frac{z}{z - a}\right) - \frac{t}{z - a}\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 99.9%

         \[\leadsto y \cdot \color{blue}{\left(\frac{x}{y} + \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\right)} \]

      2. div-sub 99.9%

         \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\frac{z - t}{z - a}}\right) \]

   5. Simplified 99.9%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} + \frac{z - t}{z - a}\right)} \]

   6. Taylor expanded in x around 0 87.6%

      \[\leadsto y \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{t}{z - a}\right)} \]
   7. Step-by-step derivation

      1. div-sub 87.6%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{z - a}} \]

   8. Simplified 87.6%

      \[\leadsto y \cdot \color{blue}{\frac{z - t}{z - a}} \]

   if -5.00000000000000029e278 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 9.99999999999999986e306

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   if 9.99999999999999986e306 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 36.6%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 36.6%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{z - a}} \]
   4. Step-by-step derivation

      1. associate-*l/ 87.4%

         \[\leadsto \color{blue}{\frac{y}{z - a} \cdot \left(z - t\right)} \]

   5. Simplified 87.4%

      \[\leadsto \color{blue}{\frac{y}{z - a} \cdot \left(z - t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -5 \cdot 10^{+278}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq 10^{+307}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-12}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+66} \lor \neg \left(y \leq 1.4 \cdot 10^{+130}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{1}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- z a)))))
   (if (<= y -7e+25)
     t_1
     (if (<= y 1.35e-12)
       (+ y x)
       (if (or (<= y 3.8e+66) (not (<= y 1.4e+130)))
         t_1
         (+ x (/ 1.0 (/ 1.0 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (z - a));
	double tmp;
	if (y <= -7e+25) {
		tmp = t_1;
	} else if (y <= 1.35e-12) {
		tmp = y + x;
	} else if ((y <= 3.8e+66) || !(y <= 1.4e+130)) {
		tmp = t_1;
	} else {
		tmp = x + (1.0 / (1.0 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (z - a))
    if (y <= (-7d+25)) then
        tmp = t_1
    else if (y <= 1.35d-12) then
        tmp = y + x
    else if ((y <= 3.8d+66) .or. (.not. (y <= 1.4d+130))) then
        tmp = t_1
    else
        tmp = x + (1.0d0 / (1.0d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (z - a));
	double tmp;
	if (y <= -7e+25) {
		tmp = t_1;
	} else if (y <= 1.35e-12) {
		tmp = y + x;
	} else if ((y <= 3.8e+66) || !(y <= 1.4e+130)) {
		tmp = t_1;
	} else {
		tmp = x + (1.0 / (1.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (z - a))
	tmp = 0
	if y <= -7e+25:
		tmp = t_1
	elif y <= 1.35e-12:
		tmp = y + x
	elif (y <= 3.8e+66) or not (y <= 1.4e+130):
		tmp = t_1
	else:
		tmp = x + (1.0 / (1.0 / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(z - a)))
	tmp = 0.0
	if (y <= -7e+25)
		tmp = t_1;
	elseif (y <= 1.35e-12)
		tmp = Float64(y + x);
	elseif ((y <= 3.8e+66) || !(y <= 1.4e+130))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(1.0 / Float64(1.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (z - a));
	tmp = 0.0;
	if (y <= -7e+25)
		tmp = t_1;
	elseif (y <= 1.35e-12)
		tmp = y + x;
	elseif ((y <= 3.8e+66) || ~((y <= 1.4e+130)))
		tmp = t_1;
	else
		tmp = x + (1.0 / (1.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+25], t$95$1, If[LessEqual[y, 1.35e-12], N[(y + x), $MachinePrecision], If[Or[LessEqual[y, 3.8e+66], N[Not[LessEqual[y, 1.4e+130]], $MachinePrecision]], t$95$1, N[(x + N[(1.0 / N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.99999999999999999e25 or 1.3499999999999999e-12 < y < 3.8000000000000002e66 or 1.3999999999999999e130 < y

   1. Initial program 69.6%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.7%

      \[\leadsto \color{blue}{y \cdot \left(\left(\frac{x}{y} + \frac{z}{z - a}\right) - \frac{t}{z - a}\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 99.7%

         \[\leadsto y \cdot \color{blue}{\left(\frac{x}{y} + \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\right)} \]

      2. div-sub 99.7%

         \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\frac{z - t}{z - a}}\right) \]

   5. Simplified 99.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} + \frac{z - t}{z - a}\right)} \]

   6. Taylor expanded in x around 0 83.1%

      \[\leadsto y \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{t}{z - a}\right)} \]
   7. Step-by-step derivation

      1. div-sub 83.1%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{z - a}} \]

   8. Simplified 83.1%

      \[\leadsto y \cdot \color{blue}{\frac{z - t}{z - a}} \]

   if -6.99999999999999999e25 < y < 1.3499999999999999e-12

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 80.0%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 80.0%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 80.0%

      \[\leadsto \color{blue}{y + x} \]

   if 3.8000000000000002e66 < y < 1.3999999999999999e130

   1. Initial program 63.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 63.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. inv-pow 63.1%

         \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]

   4. Applied egg-rr 63.1%

      \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 63.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. associate-/r* 99.8%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{z - a}{y}}{z - t}}} \]

   6. Simplified 99.8%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{z - a}{y}}{z - t}}} \]

   7. Taylor expanded in z around inf 75.4%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-12}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+66} \lor \neg \left(y \leq 1.4 \cdot 10^{+130}\right):\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{1}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-11}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+66}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+130}:\\ \;\;\;\;x + \frac{1}{\frac{1}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- z a)))))
   (if (<= y -1.7e+23)
     t_1
     (if (<= y 7e-11)
       (+ y x)
       (if (<= y 3.8e+66)
         (* (- z t) (/ y (- z a)))
         (if (<= y 1.35e+130) (+ x (/ 1.0 (/ 1.0 y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (z - a));
	double tmp;
	if (y <= -1.7e+23) {
		tmp = t_1;
	} else if (y <= 7e-11) {
		tmp = y + x;
	} else if (y <= 3.8e+66) {
		tmp = (z - t) * (y / (z - a));
	} else if (y <= 1.35e+130) {
		tmp = x + (1.0 / (1.0 / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (z - a))
    if (y <= (-1.7d+23)) then
        tmp = t_1
    else if (y <= 7d-11) then
        tmp = y + x
    else if (y <= 3.8d+66) then
        tmp = (z - t) * (y / (z - a))
    else if (y <= 1.35d+130) then
        tmp = x + (1.0d0 / (1.0d0 / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (z - a));
	double tmp;
	if (y <= -1.7e+23) {
		tmp = t_1;
	} else if (y <= 7e-11) {
		tmp = y + x;
	} else if (y <= 3.8e+66) {
		tmp = (z - t) * (y / (z - a));
	} else if (y <= 1.35e+130) {
		tmp = x + (1.0 / (1.0 / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (z - a))
	tmp = 0
	if y <= -1.7e+23:
		tmp = t_1
	elif y <= 7e-11:
		tmp = y + x
	elif y <= 3.8e+66:
		tmp = (z - t) * (y / (z - a))
	elif y <= 1.35e+130:
		tmp = x + (1.0 / (1.0 / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(z - a)))
	tmp = 0.0
	if (y <= -1.7e+23)
		tmp = t_1;
	elseif (y <= 7e-11)
		tmp = Float64(y + x);
	elseif (y <= 3.8e+66)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	elseif (y <= 1.35e+130)
		tmp = Float64(x + Float64(1.0 / Float64(1.0 / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (z - a));
	tmp = 0.0;
	if (y <= -1.7e+23)
		tmp = t_1;
	elseif (y <= 7e-11)
		tmp = y + x;
	elseif (y <= 3.8e+66)
		tmp = (z - t) * (y / (z - a));
	elseif (y <= 1.35e+130)
		tmp = x + (1.0 / (1.0 / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+23], t$95$1, If[LessEqual[y, 7e-11], N[(y + x), $MachinePrecision], If[LessEqual[y, 3.8e+66], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+130], N[(x + N[(1.0 / N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.69999999999999996e23 or 1.3499999999999999e130 < y

   1. Initial program 64.7%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.6%

      \[\leadsto \color{blue}{y \cdot \left(\left(\frac{x}{y} + \frac{z}{z - a}\right) - \frac{t}{z - a}\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 99.6%

         \[\leadsto y \cdot \color{blue}{\left(\frac{x}{y} + \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\right)} \]

      2. div-sub 99.6%

         \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\frac{z - t}{z - a}}\right) \]

   5. Simplified 99.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} + \frac{z - t}{z - a}\right)} \]

   6. Taylor expanded in x around 0 84.4%

      \[\leadsto y \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{t}{z - a}\right)} \]
   7. Step-by-step derivation

      1. div-sub 84.4%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{z - a}} \]

   8. Simplified 84.4%

      \[\leadsto y \cdot \color{blue}{\frac{z - t}{z - a}} \]

   if -1.69999999999999996e23 < y < 7.00000000000000038e-11

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 80.0%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 80.0%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 80.0%

      \[\leadsto \color{blue}{y + x} \]

   if 7.00000000000000038e-11 < y < 3.8000000000000002e66

   1. Initial program 94.8%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 71.8%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{z - a}} \]
   4. Step-by-step derivation

      1. associate-*l/ 76.9%

         \[\leadsto \color{blue}{\frac{y}{z - a} \cdot \left(z - t\right)} \]

   5. Simplified 76.9%

      \[\leadsto \color{blue}{\frac{y}{z - a} \cdot \left(z - t\right)} \]

   if 3.8000000000000002e66 < y < 1.3499999999999999e130

   1. Initial program 63.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 63.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. inv-pow 63.1%

         \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]

   4. Applied egg-rr 63.1%

      \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 63.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. associate-/r* 99.8%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{z - a}{y}}{z - t}}} \]

   6. Simplified 99.8%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{z - a}{y}}{z - t}}} \]

   7. Taylor expanded in z around inf 75.4%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-11}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+66}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+130}:\\ \;\;\;\;x + \frac{1}{\frac{1}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{z - a}\\ t_2 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{+65}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- z a))))) (t_2 (* y (/ (- z t) (- z a)))))
   (if (<= y -8.5e+52)
     t_2
     (if (<= y 2.3e-9)
       t_1
       (if (<= y 5.9e+65)
         (* (- z t) (/ y (- z a)))
         (if (<= y 1.8e+130) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double t_2 = y * ((z - t) / (z - a));
	double tmp;
	if (y <= -8.5e+52) {
		tmp = t_2;
	} else if (y <= 2.3e-9) {
		tmp = t_1;
	} else if (y <= 5.9e+65) {
		tmp = (z - t) * (y / (z - a));
	} else if (y <= 1.8e+130) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (z / (z - a)))
    t_2 = y * ((z - t) / (z - a))
    if (y <= (-8.5d+52)) then
        tmp = t_2
    else if (y <= 2.3d-9) then
        tmp = t_1
    else if (y <= 5.9d+65) then
        tmp = (z - t) * (y / (z - a))
    else if (y <= 1.8d+130) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double t_2 = y * ((z - t) / (z - a));
	double tmp;
	if (y <= -8.5e+52) {
		tmp = t_2;
	} else if (y <= 2.3e-9) {
		tmp = t_1;
	} else if (y <= 5.9e+65) {
		tmp = (z - t) * (y / (z - a));
	} else if (y <= 1.8e+130) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / (z - a)))
	t_2 = y * ((z - t) / (z - a))
	tmp = 0
	if y <= -8.5e+52:
		tmp = t_2
	elif y <= 2.3e-9:
		tmp = t_1
	elif y <= 5.9e+65:
		tmp = (z - t) * (y / (z - a))
	elif y <= 1.8e+130:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / Float64(z - a))))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(z - a)))
	tmp = 0.0
	if (y <= -8.5e+52)
		tmp = t_2;
	elseif (y <= 2.3e-9)
		tmp = t_1;
	elseif (y <= 5.9e+65)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	elseif (y <= 1.8e+130)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / (z - a)));
	t_2 = y * ((z - t) / (z - a));
	tmp = 0.0;
	if (y <= -8.5e+52)
		tmp = t_2;
	elseif (y <= 2.3e-9)
		tmp = t_1;
	elseif (y <= 5.9e+65)
		tmp = (z - t) * (y / (z - a));
	elseif (y <= 1.8e+130)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+52], t$95$2, If[LessEqual[y, 2.3e-9], t$95$1, If[LessEqual[y, 5.9e+65], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+130], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.49999999999999994e52 or 1.8000000000000001e130 < y

   1. Initial program 62.0%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.6%

      \[\leadsto \color{blue}{y \cdot \left(\left(\frac{x}{y} + \frac{z}{z - a}\right) - \frac{t}{z - a}\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 99.6%

         \[\leadsto y \cdot \color{blue}{\left(\frac{x}{y} + \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\right)} \]

      2. div-sub 99.6%

         \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\frac{z - t}{z - a}}\right) \]

   5. Simplified 99.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} + \frac{z - t}{z - a}\right)} \]

   6. Taylor expanded in x around 0 85.3%

      \[\leadsto y \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{t}{z - a}\right)} \]
   7. Step-by-step derivation

      1. div-sub 85.3%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{z - a}} \]

   8. Simplified 85.3%

      \[\leadsto y \cdot \color{blue}{\frac{z - t}{z - a}} \]

   if -8.49999999999999994e52 < y < 2.2999999999999999e-9 or 5.9000000000000003e65 < y < 1.8000000000000001e130

   1. Initial program 95.3%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 95.3%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. inv-pow 95.3%

         \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]

   4. Applied egg-rr 95.3%

      \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 95.3%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. associate-/r* 98.0%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{z - a}{y}}{z - t}}} \]

   6. Simplified 98.0%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{z - a}{y}}{z - t}}} \]

   7. Taylor expanded in t around 0 80.5%

      \[\leadsto \color{blue}{x + \frac{y \cdot z}{z - a}} \]
   8. Step-by-step derivation

      1. +-commutative 80.5%

         \[\leadsto \color{blue}{\frac{y \cdot z}{z - a} + x} \]

      2. associate-/l* 85.2%

         \[\leadsto \color{blue}{y \cdot \frac{z}{z - a}} + x \]

   9. Simplified 85.2%

      \[\leadsto \color{blue}{y \cdot \frac{z}{z - a} + x} \]

   if 2.2999999999999999e-9 < y < 5.9000000000000003e65

   1. Initial program 99.8%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{z - a}} \]
   4. Step-by-step derivation

      1. associate-*l/ 81.8%

         \[\leadsto \color{blue}{\frac{y}{z - a} \cdot \left(z - t\right)} \]

   5. Simplified 81.8%

      \[\leadsto \color{blue}{\frac{y}{z - a} \cdot \left(z - t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-9}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{+65}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+130}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 0.34:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+141} \lor \neg \left(z \leq 2.7 \cdot 10^{+181}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.2e-41)
   (+ y x)
   (if (<= z 0.34)
     (+ x (* t (/ y a)))
     (if (or (<= z 1.45e+141) (not (<= z 2.7e+181)))
       (+ y x)
       (- x (* y (/ t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e-41) {
		tmp = y + x;
	} else if (z <= 0.34) {
		tmp = x + (t * (y / a));
	} else if ((z <= 1.45e+141) || !(z <= 2.7e+181)) {
		tmp = y + x;
	} else {
		tmp = x - (y * (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.2d-41)) then
        tmp = y + x
    else if (z <= 0.34d0) then
        tmp = x + (t * (y / a))
    else if ((z <= 1.45d+141) .or. (.not. (z <= 2.7d+181))) then
        tmp = y + x
    else
        tmp = x - (y * (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e-41) {
		tmp = y + x;
	} else if (z <= 0.34) {
		tmp = x + (t * (y / a));
	} else if ((z <= 1.45e+141) || !(z <= 2.7e+181)) {
		tmp = y + x;
	} else {
		tmp = x - (y * (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.2e-41:
		tmp = y + x
	elif z <= 0.34:
		tmp = x + (t * (y / a))
	elif (z <= 1.45e+141) or not (z <= 2.7e+181):
		tmp = y + x
	else:
		tmp = x - (y * (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.2e-41)
		tmp = Float64(y + x);
	elseif (z <= 0.34)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif ((z <= 1.45e+141) || !(z <= 2.7e+181))
		tmp = Float64(y + x);
	else
		tmp = Float64(x - Float64(y * Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.2e-41)
		tmp = y + x;
	elseif (z <= 0.34)
		tmp = x + (t * (y / a));
	elseif ((z <= 1.45e+141) || ~((z <= 2.7e+181)))
		tmp = y + x;
	else
		tmp = x - (y * (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.2e-41], N[(y + x), $MachinePrecision], If[LessEqual[z, 0.34], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.45e+141], N[Not[LessEqual[z, 2.7e+181]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.20000000000000028e-41 or 0.340000000000000024 < z < 1.45000000000000003e141 or 2.70000000000000007e181 < z

   1. Initial program 74.7%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.1%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 78.1%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 78.1%

      \[\leadsto \color{blue}{y + x} \]

   if -8.20000000000000028e-41 < z < 0.340000000000000024

   1. Initial program 96.6%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 71.8%

      \[\leadsto \color{blue}{x + \frac{t \cdot y}{a}} \]
   4. Step-by-step derivation

      1. +-commutative 71.8%

         \[\leadsto \color{blue}{\frac{t \cdot y}{a} + x} \]

      2. associate-/l* 72.3%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} + x \]

   5. Simplified 72.3%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a} + x} \]

   if 1.45000000000000003e141 < z < 2.70000000000000007e181

   1. Initial program 67.4%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 67.4%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(z - t\right)}{z}} \]
   4. Step-by-step derivation

      1. +-commutative 67.4%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{z} + x} \]

      2. associate-/l* 83.6%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{z}} + x \]

   5. Simplified 83.6%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{z} + x} \]

   6. Taylor expanded in z around 0 86.4%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \frac{t}{z}\right)} + x \]
   7. Step-by-step derivation

      1. neg-mul-1 86.4%

         \[\leadsto y \cdot \color{blue}{\left(-\frac{t}{z}\right)} + x \]

      2. distribute-neg-frac2 86.4%

         \[\leadsto y \cdot \color{blue}{\frac{t}{-z}} + x \]

   8. Simplified 86.4%

      \[\leadsto y \cdot \color{blue}{\frac{t}{-z}} + x \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 0.34:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+141} \lor \neg \left(z \leq 2.7 \cdot 10^{+181}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 11.5:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+125} \lor \neg \left(z \leq 7.6 \cdot 10^{+182}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.8e-41)
   (+ y x)
   (if (<= z 11.5)
     (+ x (* t (/ y a)))
     (if (or (<= z 1.38e+125) (not (<= z 7.6e+182)))
       (+ y x)
       (- x (* t (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e-41) {
		tmp = y + x;
	} else if (z <= 11.5) {
		tmp = x + (t * (y / a));
	} else if ((z <= 1.38e+125) || !(z <= 7.6e+182)) {
		tmp = y + x;
	} else {
		tmp = x - (t * (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.8d-41)) then
        tmp = y + x
    else if (z <= 11.5d0) then
        tmp = x + (t * (y / a))
    else if ((z <= 1.38d+125) .or. (.not. (z <= 7.6d+182))) then
        tmp = y + x
    else
        tmp = x - (t * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e-41) {
		tmp = y + x;
	} else if (z <= 11.5) {
		tmp = x + (t * (y / a));
	} else if ((z <= 1.38e+125) || !(z <= 7.6e+182)) {
		tmp = y + x;
	} else {
		tmp = x - (t * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.8e-41:
		tmp = y + x
	elif z <= 11.5:
		tmp = x + (t * (y / a))
	elif (z <= 1.38e+125) or not (z <= 7.6e+182):
		tmp = y + x
	else:
		tmp = x - (t * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.8e-41)
		tmp = Float64(y + x);
	elseif (z <= 11.5)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif ((z <= 1.38e+125) || !(z <= 7.6e+182))
		tmp = Float64(y + x);
	else
		tmp = Float64(x - Float64(t * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.8e-41)
		tmp = y + x;
	elseif (z <= 11.5)
		tmp = x + (t * (y / a));
	elseif ((z <= 1.38e+125) || ~((z <= 7.6e+182)))
		tmp = y + x;
	else
		tmp = x - (t * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.8e-41], N[(y + x), $MachinePrecision], If[LessEqual[z, 11.5], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.38e+125], N[Not[LessEqual[z, 7.6e+182]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.7999999999999999e-41 or 11.5 < z < 1.38e125 or 7.60000000000000025e182 < z

   1. Initial program 74.7%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.1%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 78.1%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 78.1%

      \[\leadsto \color{blue}{y + x} \]

   if -8.7999999999999999e-41 < z < 11.5

   1. Initial program 96.6%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 71.8%

      \[\leadsto \color{blue}{x + \frac{t \cdot y}{a}} \]
   4. Step-by-step derivation

      1. +-commutative 71.8%

         \[\leadsto \color{blue}{\frac{t \cdot y}{a} + x} \]

      2. associate-/l* 72.3%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} + x \]

   5. Simplified 72.3%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a} + x} \]

   if 1.38e125 < z < 7.60000000000000025e182

   1. Initial program 67.4%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 67.4%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(z - t\right)}{z}} \]
   4. Step-by-step derivation

      1. +-commutative 67.4%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{z} + x} \]

      2. associate-/l* 83.6%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{z}} + x \]

   5. Simplified 83.6%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{z} + x} \]

   6. Taylor expanded in z around 0 70.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{z}} + x \]
   7. Step-by-step derivation

      1. mul-1-neg 70.3%

         \[\leadsto \color{blue}{\left(-\frac{t \cdot y}{z}\right)} + x \]

      2. associate-/l* 86.6%

         \[\leadsto \left(-\color{blue}{t \cdot \frac{y}{z}}\right) + x \]

      3. distribute-lft-neg-in 86.6%

         \[\leadsto \color{blue}{\left(-t\right) \cdot \frac{y}{z}} + x \]

   8. Simplified 86.6%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \frac{y}{z}} + x \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 11.5:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+125} \lor \neg \left(z \leq 7.6 \cdot 10^{+182}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-t\right) \cdot \frac{y}{z}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+181}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+279}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t) (/ y z))))
   (if (<= t -6.2e+185)
     t_1
     (if (<= t 3.4e+181)
       (+ y x)
       (if (<= t 1.05e+273) t_1 (if (<= t 3.9e+279) (+ y x) (/ (* y t) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t * (y / z);
	double tmp;
	if (t <= -6.2e+185) {
		tmp = t_1;
	} else if (t <= 3.4e+181) {
		tmp = y + x;
	} else if (t <= 1.05e+273) {
		tmp = t_1;
	} else if (t <= 3.9e+279) {
		tmp = y + x;
	} else {
		tmp = (y * t) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -t * (y / z)
    if (t <= (-6.2d+185)) then
        tmp = t_1
    else if (t <= 3.4d+181) then
        tmp = y + x
    else if (t <= 1.05d+273) then
        tmp = t_1
    else if (t <= 3.9d+279) then
        tmp = y + x
    else
        tmp = (y * t) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -t * (y / z);
	double tmp;
	if (t <= -6.2e+185) {
		tmp = t_1;
	} else if (t <= 3.4e+181) {
		tmp = y + x;
	} else if (t <= 1.05e+273) {
		tmp = t_1;
	} else if (t <= 3.9e+279) {
		tmp = y + x;
	} else {
		tmp = (y * t) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t * (y / z)
	tmp = 0
	if t <= -6.2e+185:
		tmp = t_1
	elif t <= 3.4e+181:
		tmp = y + x
	elif t <= 1.05e+273:
		tmp = t_1
	elif t <= 3.9e+279:
		tmp = y + x
	else:
		tmp = (y * t) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) * Float64(y / z))
	tmp = 0.0
	if (t <= -6.2e+185)
		tmp = t_1;
	elseif (t <= 3.4e+181)
		tmp = Float64(y + x);
	elseif (t <= 1.05e+273)
		tmp = t_1;
	elseif (t <= 3.9e+279)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(y * t) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t * (y / z);
	tmp = 0.0;
	if (t <= -6.2e+185)
		tmp = t_1;
	elseif (t <= 3.4e+181)
		tmp = y + x;
	elseif (t <= 1.05e+273)
		tmp = t_1;
	elseif (t <= 3.9e+279)
		tmp = y + x;
	else
		tmp = (y * t) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e+185], t$95$1, If[LessEqual[t, 3.4e+181], N[(y + x), $MachinePrecision], If[LessEqual[t, 1.05e+273], t$95$1, If[LessEqual[t, 3.9e+279], N[(y + x), $MachinePrecision], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.19999999999999999e185 or 3.40000000000000031e181 < t < 1.05000000000000001e273

   1. Initial program 80.6%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 87.0%

      \[\leadsto \color{blue}{y \cdot \left(\left(\frac{x}{y} + \frac{z}{z - a}\right) - \frac{t}{z - a}\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 87.0%

         \[\leadsto y \cdot \color{blue}{\left(\frac{x}{y} + \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\right)} \]

      2. div-sub 87.0%

         \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\frac{z - t}{z - a}}\right) \]

   5. Simplified 87.0%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} + \frac{z - t}{z - a}\right)} \]

   6. Taylor expanded in t around inf 71.0%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \frac{t}{z - a}\right)} \]
   7. Step-by-step derivation

      1. associate-*r/ 71.0%

         \[\leadsto y \cdot \color{blue}{\frac{-1 \cdot t}{z - a}} \]

      2. mul-1-neg 71.0%

         \[\leadsto y \cdot \frac{\color{blue}{-t}}{z - a} \]

   8. Simplified 71.0%

      \[\leadsto y \cdot \color{blue}{\frac{-t}{z - a}} \]

   9. Taylor expanded in z around inf 51.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 51.0%

          \[\leadsto \color{blue}{-\frac{t \cdot y}{z}} \]

       2. associate-/l* 57.4%

          \[\leadsto -\color{blue}{t \cdot \frac{y}{z}} \]

       3. distribute-lft-neg-in 57.4%

          \[\leadsto \color{blue}{\left(-t\right) \cdot \frac{y}{z}} \]

   11. Simplified 57.4%

       \[\leadsto \color{blue}{\left(-t\right) \cdot \frac{y}{z}} \]

   if -6.19999999999999999e185 < t < 3.40000000000000031e181 or 1.05000000000000001e273 < t < 3.90000000000000019e279

   1. Initial program 84.3%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 71.0%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 71.0%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 71.0%

      \[\leadsto \color{blue}{y + x} \]

   if 3.90000000000000019e279 < t

   1. Initial program 86.7%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 73.2%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{z - a}} \]

   4. Taylor expanded in z around 0 57.9%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+185}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+181}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+273}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+279}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+183}:\\ \;\;\;\;\frac{t}{\frac{z}{-y}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+180}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+274}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+278}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5e+183)
   (/ t (/ z (- y)))
   (if (<= t 3.5e+180)
     (+ y x)
     (if (<= t 2.2e+274)
       (* (- t) (/ y z))
       (if (<= t 5.4e+278) (+ y x) (/ (* y t) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5e+183) {
		tmp = t / (z / -y);
	} else if (t <= 3.5e+180) {
		tmp = y + x;
	} else if (t <= 2.2e+274) {
		tmp = -t * (y / z);
	} else if (t <= 5.4e+278) {
		tmp = y + x;
	} else {
		tmp = (y * t) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5d+183)) then
        tmp = t / (z / -y)
    else if (t <= 3.5d+180) then
        tmp = y + x
    else if (t <= 2.2d+274) then
        tmp = -t * (y / z)
    else if (t <= 5.4d+278) then
        tmp = y + x
    else
        tmp = (y * t) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5e+183) {
		tmp = t / (z / -y);
	} else if (t <= 3.5e+180) {
		tmp = y + x;
	} else if (t <= 2.2e+274) {
		tmp = -t * (y / z);
	} else if (t <= 5.4e+278) {
		tmp = y + x;
	} else {
		tmp = (y * t) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5e+183:
		tmp = t / (z / -y)
	elif t <= 3.5e+180:
		tmp = y + x
	elif t <= 2.2e+274:
		tmp = -t * (y / z)
	elif t <= 5.4e+278:
		tmp = y + x
	else:
		tmp = (y * t) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5e+183)
		tmp = Float64(t / Float64(z / Float64(-y)));
	elseif (t <= 3.5e+180)
		tmp = Float64(y + x);
	elseif (t <= 2.2e+274)
		tmp = Float64(Float64(-t) * Float64(y / z));
	elseif (t <= 5.4e+278)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(y * t) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5e+183)
		tmp = t / (z / -y);
	elseif (t <= 3.5e+180)
		tmp = y + x;
	elseif (t <= 2.2e+274)
		tmp = -t * (y / z);
	elseif (t <= 5.4e+278)
		tmp = y + x;
	else
		tmp = (y * t) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5e+183], N[(t / N[(z / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+180], N[(y + x), $MachinePrecision], If[LessEqual[t, 2.2e+274], N[((-t) * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e+278], N[(y + x), $MachinePrecision], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.00000000000000009e183

   1. Initial program 83.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 86.4%

      \[\leadsto \color{blue}{y \cdot \left(\left(\frac{x}{y} + \frac{z}{z - a}\right) - \frac{t}{z - a}\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 86.4%

         \[\leadsto y \cdot \color{blue}{\left(\frac{x}{y} + \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\right)} \]

      2. div-sub 86.4%

         \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\frac{z - t}{z - a}}\right) \]

   5. Simplified 86.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} + \frac{z - t}{z - a}\right)} \]

   6. Taylor expanded in t around inf 72.1%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \frac{t}{z - a}\right)} \]
   7. Step-by-step derivation

      1. associate-*r/ 72.1%

         \[\leadsto y \cdot \color{blue}{\frac{-1 \cdot t}{z - a}} \]

      2. mul-1-neg 72.1%

         \[\leadsto y \cdot \frac{\color{blue}{-t}}{z - a} \]

   8. Simplified 72.1%

      \[\leadsto y \cdot \color{blue}{\frac{-t}{z - a}} \]
   9. Step-by-step derivation

      1. *-commutative 72.1%

         \[\leadsto \color{blue}{\frac{-t}{z - a} \cdot y} \]

      2. div-inv 72.0%

         \[\leadsto \color{blue}{\left(\left(-t\right) \cdot \frac{1}{z - a}\right)} \cdot y \]

      3. associate-*l* 75.4%

         \[\leadsto \color{blue}{\left(-t\right) \cdot \left(\frac{1}{z - a} \cdot y\right)} \]

      4. add-sqr-sqrt 75.2%

         \[\leadsto \color{blue}{\left(\sqrt{-t} \cdot \sqrt{-t}\right)} \cdot \left(\frac{1}{z - a} \cdot y\right) \]

      5. sqrt-unprod 44.6%

         \[\leadsto \color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}} \cdot \left(\frac{1}{z - a} \cdot y\right) \]

      6. sqr-neg 44.6%

         \[\leadsto \sqrt{\color{blue}{t \cdot t}} \cdot \left(\frac{1}{z - a} \cdot y\right) \]

      7. sqrt-unprod 0.0%

         \[\leadsto \color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)} \cdot \left(\frac{1}{z - a} \cdot y\right) \]

      8. add-sqr-sqrt 1.3%

         \[\leadsto \color{blue}{t} \cdot \left(\frac{1}{z - a} \cdot y\right) \]

      9. associate-/r/ 1.3%

         \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{z - a}{y}}} \]

      10. div-inv 1.3%

          \[\leadsto \color{blue}{\frac{t}{\frac{z - a}{y}}} \]

      11. frac-2neg 1.3%

          \[\leadsto \color{blue}{\frac{-t}{-\frac{z - a}{y}}} \]

      12. add-sqr-sqrt 1.3%

          \[\leadsto \frac{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}}{-\frac{z - a}{y}} \]

      13. sqrt-unprod 0.8%

          \[\leadsto \frac{\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}}{-\frac{z - a}{y}} \]

      14. sqr-neg 0.8%

          \[\leadsto \frac{\sqrt{\color{blue}{t \cdot t}}}{-\frac{z - a}{y}} \]

      15. sqrt-unprod 0.0%

          \[\leadsto \frac{\color{blue}{\sqrt{t} \cdot \sqrt{t}}}{-\frac{z - a}{y}} \]

      16. add-sqr-sqrt 75.5%

          \[\leadsto \frac{\color{blue}{t}}{-\frac{z - a}{y}} \]

      17. distribute-neg-frac2 75.5%

          \[\leadsto \frac{t}{\color{blue}{\frac{z - a}{-y}}} \]

   10. Applied egg-rr 75.5%

       \[\leadsto \color{blue}{\frac{t}{\frac{z - a}{-y}}} \]

   11. Taylor expanded in z around inf 55.5%

       \[\leadsto \frac{t}{\color{blue}{-1 \cdot \frac{z}{y}}} \]
   12. Step-by-step derivation

       1. associate-*r/ 55.5%

          \[\leadsto \frac{t}{\color{blue}{\frac{-1 \cdot z}{y}}} \]

       2. neg-mul-1 55.5%

          \[\leadsto \frac{t}{\frac{\color{blue}{-z}}{y}} \]

   13. Simplified 55.5%

       \[\leadsto \frac{t}{\color{blue}{\frac{-z}{y}}} \]

   if -5.00000000000000009e183 < t < 3.4999999999999998e180 or 2.2000000000000001e274 < t < 5.40000000000000021e278

   1. Initial program 84.3%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 71.0%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 71.0%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 71.0%

      \[\leadsto \color{blue}{y + x} \]

   if 3.4999999999999998e180 < t < 2.2000000000000001e274

   1. Initial program 76.3%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 88.0%

      \[\leadsto \color{blue}{y \cdot \left(\left(\frac{x}{y} + \frac{z}{z - a}\right) - \frac{t}{z - a}\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 88.0%

         \[\leadsto y \cdot \color{blue}{\left(\frac{x}{y} + \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\right)} \]

      2. div-sub 88.0%

         \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\frac{z - t}{z - a}}\right) \]

   5. Simplified 88.0%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} + \frac{z - t}{z - a}\right)} \]

   6. Taylor expanded in t around inf 69.1%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \frac{t}{z - a}\right)} \]
   7. Step-by-step derivation

      1. associate-*r/ 69.1%

         \[\leadsto y \cdot \color{blue}{\frac{-1 \cdot t}{z - a}} \]

      2. mul-1-neg 69.1%

         \[\leadsto y \cdot \frac{\color{blue}{-t}}{z - a} \]

   8. Simplified 69.1%

      \[\leadsto y \cdot \color{blue}{\frac{-t}{z - a}} \]

   9. Taylor expanded in z around inf 55.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 55.0%

          \[\leadsto \color{blue}{-\frac{t \cdot y}{z}} \]

       2. associate-/l* 60.8%

          \[\leadsto -\color{blue}{t \cdot \frac{y}{z}} \]

       3. distribute-lft-neg-in 60.8%

          \[\leadsto \color{blue}{\left(-t\right) \cdot \frac{y}{z}} \]

   11. Simplified 60.8%

       \[\leadsto \color{blue}{\left(-t\right) \cdot \frac{y}{z}} \]

   if 5.40000000000000021e278 < t

   1. Initial program 86.7%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 73.2%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{z - a}} \]

   4. Taylor expanded in z around 0 57.9%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+183}:\\ \;\;\;\;\frac{t}{\frac{z}{-y}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+180}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+274}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+278}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 78.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+81}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 10^{-90}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-56}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.8e+81)
   (+ x (* t (/ y a)))
   (if (<= a 1e-90)
     (+ x (* y (/ (- z t) z)))
     (if (<= a 2.9e-56) (* y (/ (- z t) (- z a))) (+ x (* y (/ z (- z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.8e+81) {
		tmp = x + (t * (y / a));
	} else if (a <= 1e-90) {
		tmp = x + (y * ((z - t) / z));
	} else if (a <= 2.9e-56) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.8d+81)) then
        tmp = x + (t * (y / a))
    else if (a <= 1d-90) then
        tmp = x + (y * ((z - t) / z))
    else if (a <= 2.9d-56) then
        tmp = y * ((z - t) / (z - a))
    else
        tmp = x + (y * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.8e+81) {
		tmp = x + (t * (y / a));
	} else if (a <= 1e-90) {
		tmp = x + (y * ((z - t) / z));
	} else if (a <= 2.9e-56) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.8e+81:
		tmp = x + (t * (y / a))
	elif a <= 1e-90:
		tmp = x + (y * ((z - t) / z))
	elif a <= 2.9e-56:
		tmp = y * ((z - t) / (z - a))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.8e+81)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (a <= 1e-90)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	elseif (a <= 2.9e-56)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(z - a)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.8e+81)
		tmp = x + (t * (y / a));
	elseif (a <= 1e-90)
		tmp = x + (y * ((z - t) / z));
	elseif (a <= 2.9e-56)
		tmp = y * ((z - t) / (z - a));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.8e+81], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-90], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e-56], N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.80000000000000005e81

   1. Initial program 83.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 75.5%

      \[\leadsto \color{blue}{x + \frac{t \cdot y}{a}} \]
   4. Step-by-step derivation

      1. +-commutative 75.5%

         \[\leadsto \color{blue}{\frac{t \cdot y}{a} + x} \]

      2. associate-/l* 79.9%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} + x \]

   5. Simplified 79.9%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a} + x} \]

   if -6.80000000000000005e81 < a < 9.99999999999999995e-91

   1. Initial program 88.5%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 79.7%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(z - t\right)}{z}} \]
   4. Step-by-step derivation

      1. +-commutative 79.7%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{z} + x} \]

      2. associate-/l* 88.9%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{z}} + x \]

   5. Simplified 88.9%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{z} + x} \]

   if 9.99999999999999995e-91 < a < 2.89999999999999991e-56

   1. Initial program 86.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(\frac{x}{y} + \frac{z}{z - a}\right) - \frac{t}{z - a}\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 99.9%

         \[\leadsto y \cdot \color{blue}{\left(\frac{x}{y} + \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\right)} \]

      2. div-sub 99.9%

         \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\frac{z - t}{z - a}}\right) \]

   5. Simplified 99.9%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} + \frac{z - t}{z - a}\right)} \]

   6. Taylor expanded in x around 0 95.1%

      \[\leadsto y \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{t}{z - a}\right)} \]
   7. Step-by-step derivation

      1. div-sub 95.1%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{z - a}} \]

   8. Simplified 95.1%

      \[\leadsto y \cdot \color{blue}{\frac{z - t}{z - a}} \]

   if 2.89999999999999991e-56 < a

   1. Initial program 74.0%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 74.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. inv-pow 74.1%

         \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]

   4. Applied egg-rr 74.1%

      \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 74.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. associate-/r* 99.8%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{z - a}{y}}{z - t}}} \]

   6. Simplified 99.8%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{z - a}{y}}{z - t}}} \]

   7. Taylor expanded in t around 0 65.3%

      \[\leadsto \color{blue}{x + \frac{y \cdot z}{z - a}} \]
   8. Step-by-step derivation

      1. +-commutative 65.3%

         \[\leadsto \color{blue}{\frac{y \cdot z}{z - a} + x} \]

      2. associate-/l* 84.6%

         \[\leadsto \color{blue}{y \cdot \frac{z}{z - a}} + x \]

   9. Simplified 84.6%

      \[\leadsto \color{blue}{y \cdot \frac{z}{z - a} + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+81}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 10^{-90}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-56}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 78.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+80}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.8e+80)
   (+ x (* t (/ y a)))
   (if (<= a 1.65e-90)
     (+ x (/ y (/ z (- z t))))
     (if (<= a 9.2e-58) (* y (/ (- z t) (- z a))) (+ x (* y (/ z (- z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.8e+80) {
		tmp = x + (t * (y / a));
	} else if (a <= 1.65e-90) {
		tmp = x + (y / (z / (z - t)));
	} else if (a <= 9.2e-58) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7.8d+80)) then
        tmp = x + (t * (y / a))
    else if (a <= 1.65d-90) then
        tmp = x + (y / (z / (z - t)))
    else if (a <= 9.2d-58) then
        tmp = y * ((z - t) / (z - a))
    else
        tmp = x + (y * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.8e+80) {
		tmp = x + (t * (y / a));
	} else if (a <= 1.65e-90) {
		tmp = x + (y / (z / (z - t)));
	} else if (a <= 9.2e-58) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.8e+80:
		tmp = x + (t * (y / a))
	elif a <= 1.65e-90:
		tmp = x + (y / (z / (z - t)))
	elif a <= 9.2e-58:
		tmp = y * ((z - t) / (z - a))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.8e+80)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (a <= 1.65e-90)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (a <= 9.2e-58)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(z - a)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.8e+80)
		tmp = x + (t * (y / a));
	elseif (a <= 1.65e-90)
		tmp = x + (y / (z / (z - t)));
	elseif (a <= 9.2e-58)
		tmp = y * ((z - t) / (z - a));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.8e+80], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e-90], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e-58], N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.79999999999999998e80

   1. Initial program 83.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 75.5%

      \[\leadsto \color{blue}{x + \frac{t \cdot y}{a}} \]
   4. Step-by-step derivation

      1. +-commutative 75.5%

         \[\leadsto \color{blue}{\frac{t \cdot y}{a} + x} \]

      2. associate-/l* 79.9%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} + x \]

   5. Simplified 79.9%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a} + x} \]

   if -7.79999999999999998e80 < a < 1.65e-90

   1. Initial program 88.5%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 79.7%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(z - t\right)}{z}} \]
   4. Step-by-step derivation

      1. +-commutative 79.7%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{z} + x} \]

      2. associate-/l* 88.9%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{z}} + x \]

   5. Simplified 88.9%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{z} + x} \]
   6. Step-by-step derivation

      1. clear-num 88.9%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{z}{z - t}}} + x \]

      2. un-div-inv 89.6%

         \[\leadsto \color{blue}{\frac{y}{\frac{z}{z - t}}} + x \]

   7. Applied egg-rr 89.6%

      \[\leadsto \color{blue}{\frac{y}{\frac{z}{z - t}}} + x \]

   if 1.65e-90 < a < 9.1999999999999995e-58

   1. Initial program 86.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(\frac{x}{y} + \frac{z}{z - a}\right) - \frac{t}{z - a}\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 99.9%

         \[\leadsto y \cdot \color{blue}{\left(\frac{x}{y} + \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\right)} \]

      2. div-sub 99.9%

         \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\frac{z - t}{z - a}}\right) \]

   5. Simplified 99.9%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} + \frac{z - t}{z - a}\right)} \]

   6. Taylor expanded in x around 0 95.1%

      \[\leadsto y \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{t}{z - a}\right)} \]
   7. Step-by-step derivation

      1. div-sub 95.1%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{z - a}} \]

   8. Simplified 95.1%

      \[\leadsto y \cdot \color{blue}{\frac{z - t}{z - a}} \]

   if 9.1999999999999995e-58 < a

   1. Initial program 74.0%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 74.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. inv-pow 74.1%

         \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]

   4. Applied egg-rr 74.1%

      \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 74.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. associate-/r* 99.8%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{z - a}{y}}{z - t}}} \]

   6. Simplified 99.8%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{z - a}{y}}{z - t}}} \]

   7. Taylor expanded in t around 0 65.3%

      \[\leadsto \color{blue}{x + \frac{y \cdot z}{z - a}} \]
   8. Step-by-step derivation

      1. +-commutative 65.3%

         \[\leadsto \color{blue}{\frac{y \cdot z}{z - a} + x} \]

      2. associate-/l* 84.6%

         \[\leadsto \color{blue}{y \cdot \frac{z}{z - a}} + x \]

   9. Simplified 84.6%

      \[\leadsto \color{blue}{y \cdot \frac{z}{z - a} + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+80}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 80.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+81}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.2e+81)
   (+ x (* y (/ (- t z) a)))
   (if (<= a 1.9e-90)
     (+ x (/ y (/ z (- z t))))
     (if (<= a 2.1e-57) (* y (/ (- z t) (- z a))) (+ x (* y (/ z (- z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e+81) {
		tmp = x + (y * ((t - z) / a));
	} else if (a <= 1.9e-90) {
		tmp = x + (y / (z / (z - t)));
	} else if (a <= 2.1e-57) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.2d+81)) then
        tmp = x + (y * ((t - z) / a))
    else if (a <= 1.9d-90) then
        tmp = x + (y / (z / (z - t)))
    else if (a <= 2.1d-57) then
        tmp = y * ((z - t) / (z - a))
    else
        tmp = x + (y * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e+81) {
		tmp = x + (y * ((t - z) / a));
	} else if (a <= 1.9e-90) {
		tmp = x + (y / (z / (z - t)));
	} else if (a <= 2.1e-57) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.2e+81:
		tmp = x + (y * ((t - z) / a))
	elif a <= 1.9e-90:
		tmp = x + (y / (z / (z - t)))
	elif a <= 2.1e-57:
		tmp = y * ((z - t) / (z - a))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.2e+81)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	elseif (a <= 1.9e-90)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (a <= 2.1e-57)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(z - a)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.2e+81)
		tmp = x + (y * ((t - z) / a));
	elseif (a <= 1.9e-90)
		tmp = x + (y / (z / (z - t)));
	elseif (a <= 2.1e-57)
		tmp = y * ((z - t) / (z - a));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.2e+81], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e-90], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e-57], N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.2e81

   1. Initial program 83.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 81.2%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{y \cdot \left(z - t\right)}{a}} \]
   4. Step-by-step derivation

      1. mul-1-neg 81.2%

         \[\leadsto x + \color{blue}{\left(-\frac{y \cdot \left(z - t\right)}{a}\right)} \]

      2. unsub-neg 81.2%

         \[\leadsto \color{blue}{x - \frac{y \cdot \left(z - t\right)}{a}} \]

      3. associate-/l* 87.6%

         \[\leadsto x - \color{blue}{y \cdot \frac{z - t}{a}} \]

   5. Simplified 87.6%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]

   if -3.2e81 < a < 1.9e-90

   1. Initial program 88.5%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 79.7%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(z - t\right)}{z}} \]
   4. Step-by-step derivation

      1. +-commutative 79.7%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{z} + x} \]

      2. associate-/l* 88.9%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{z}} + x \]

   5. Simplified 88.9%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{z} + x} \]
   6. Step-by-step derivation

      1. clear-num 88.9%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{z}{z - t}}} + x \]

      2. un-div-inv 89.6%

         \[\leadsto \color{blue}{\frac{y}{\frac{z}{z - t}}} + x \]

   7. Applied egg-rr 89.6%

      \[\leadsto \color{blue}{\frac{y}{\frac{z}{z - t}}} + x \]

   if 1.9e-90 < a < 2.0999999999999999e-57

   1. Initial program 86.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(\frac{x}{y} + \frac{z}{z - a}\right) - \frac{t}{z - a}\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 99.9%

         \[\leadsto y \cdot \color{blue}{\left(\frac{x}{y} + \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\right)} \]

      2. div-sub 99.9%

         \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\frac{z - t}{z - a}}\right) \]

   5. Simplified 99.9%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} + \frac{z - t}{z - a}\right)} \]

   6. Taylor expanded in x around 0 95.1%

      \[\leadsto y \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{t}{z - a}\right)} \]
   7. Step-by-step derivation

      1. div-sub 95.1%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{z - a}} \]

   8. Simplified 95.1%

      \[\leadsto y \cdot \color{blue}{\frac{z - t}{z - a}} \]

   if 2.0999999999999999e-57 < a

   1. Initial program 74.0%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 74.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. inv-pow 74.1%

         \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]

   4. Applied egg-rr 74.1%

      \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 74.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. associate-/r* 99.8%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{z - a}{y}}{z - t}}} \]

   6. Simplified 99.8%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{z - a}{y}}{z - t}}} \]

   7. Taylor expanded in t around 0 65.3%

      \[\leadsto \color{blue}{x + \frac{y \cdot z}{z - a}} \]
   8. Step-by-step derivation

      1. +-commutative 65.3%

         \[\leadsto \color{blue}{\frac{y \cdot z}{z - a} + x} \]

      2. associate-/l* 84.6%

         \[\leadsto \color{blue}{y \cdot \frac{z}{z - a}} + x \]

   9. Simplified 84.6%

      \[\leadsto \color{blue}{y \cdot \frac{z}{z - a} + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+81}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 80.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+81}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.8e+81)
   (+ x (/ (- t z) (/ a y)))
   (if (<= a 1.9e-90)
     (+ x (/ y (/ z (- z t))))
     (if (<= a 4.4e-57) (* y (/ (- z t) (- z a))) (+ x (* y (/ z (- z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.8e+81) {
		tmp = x + ((t - z) / (a / y));
	} else if (a <= 1.9e-90) {
		tmp = x + (y / (z / (z - t)));
	} else if (a <= 4.4e-57) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.8d+81)) then
        tmp = x + ((t - z) / (a / y))
    else if (a <= 1.9d-90) then
        tmp = x + (y / (z / (z - t)))
    else if (a <= 4.4d-57) then
        tmp = y * ((z - t) / (z - a))
    else
        tmp = x + (y * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.8e+81) {
		tmp = x + ((t - z) / (a / y));
	} else if (a <= 1.9e-90) {
		tmp = x + (y / (z / (z - t)));
	} else if (a <= 4.4e-57) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.8e+81:
		tmp = x + ((t - z) / (a / y))
	elif a <= 1.9e-90:
		tmp = x + (y / (z / (z - t)))
	elif a <= 4.4e-57:
		tmp = y * ((z - t) / (z - a))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.8e+81)
		tmp = Float64(x + Float64(Float64(t - z) / Float64(a / y)));
	elseif (a <= 1.9e-90)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (a <= 4.4e-57)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(z - a)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.8e+81)
		tmp = x + ((t - z) / (a / y));
	elseif (a <= 1.9e-90)
		tmp = x + (y / (z / (z - t)));
	elseif (a <= 4.4e-57)
		tmp = y * ((z - t) / (z - a));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.8e+81], N[(x + N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e-90], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.4e-57], N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.80000000000000003e81

   1. Initial program 83.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 83.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. inv-pow 83.7%

         \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]

   4. Applied egg-rr 83.7%

      \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 83.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. associate-/r* 99.7%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{z - a}{y}}{z - t}}} \]

   6. Simplified 99.7%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{z - a}{y}}{z - t}}} \]
   7. Step-by-step derivation

      1. clear-num 99.8%

         \[\leadsto x + \color{blue}{\frac{z - t}{\frac{z - a}{y}}} \]

      2. add-cube-cbrt 99.1%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}}{\frac{z - a}{y}} \]

      3. div-inv 99.0%

         \[\leadsto x + \frac{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}{\color{blue}{\left(z - a\right) \cdot \frac{1}{y}}} \]

      4. times-frac 96.8%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{z - a} \cdot \frac{\sqrt[3]{z - t}}{\frac{1}{y}}} \]

      5. pow2 96.8%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{z - t}\right)}^{2}}}{z - a} \cdot \frac{\sqrt[3]{z - t}}{\frac{1}{y}} \]

   8. Applied egg-rr 96.8%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2}}{z - a} \cdot \frac{\sqrt[3]{z - t}}{\frac{1}{y}}} \]
   9. Step-by-step derivation

      1. times-frac 99.0%

         \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2} \cdot \sqrt[3]{z - t}}{\left(z - a\right) \cdot \frac{1}{y}}} \]

      2. unpow2 99.0%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)} \cdot \sqrt[3]{z - t}}{\left(z - a\right) \cdot \frac{1}{y}} \]

      3. rem-3cbrt-lft 99.6%

         \[\leadsto x + \frac{\color{blue}{z - t}}{\left(z - a\right) \cdot \frac{1}{y}} \]

      4. associate-*r/ 99.8%

         \[\leadsto x + \frac{z - t}{\color{blue}{\frac{\left(z - a\right) \cdot 1}{y}}} \]

      5. *-rgt-identity 99.8%

         \[\leadsto x + \frac{z - t}{\frac{\color{blue}{z - a}}{y}} \]

   10. Simplified 99.8%

       \[\leadsto x + \color{blue}{\frac{z - t}{\frac{z - a}{y}}} \]

   11. Taylor expanded in z around 0 87.9%

       \[\leadsto x + \frac{z - t}{\color{blue}{-1 \cdot \frac{a}{y}}} \]
   12. Step-by-step derivation

       1. neg-mul-1 87.9%

          \[\leadsto x + \frac{z - t}{\color{blue}{-\frac{a}{y}}} \]

       2. distribute-neg-frac2 87.9%

          \[\leadsto x + \frac{z - t}{\color{blue}{\frac{a}{-y}}} \]

   13. Simplified 87.9%

       \[\leadsto x + \frac{z - t}{\color{blue}{\frac{a}{-y}}} \]

   if -1.80000000000000003e81 < a < 1.9e-90

   1. Initial program 88.5%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 79.7%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(z - t\right)}{z}} \]
   4. Step-by-step derivation

      1. +-commutative 79.7%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{z} + x} \]

      2. associate-/l* 88.9%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{z}} + x \]

   5. Simplified 88.9%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{z} + x} \]
   6. Step-by-step derivation

      1. clear-num 88.9%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{z}{z - t}}} + x \]

      2. un-div-inv 89.6%

         \[\leadsto \color{blue}{\frac{y}{\frac{z}{z - t}}} + x \]

   7. Applied egg-rr 89.6%

      \[\leadsto \color{blue}{\frac{y}{\frac{z}{z - t}}} + x \]

   if 1.9e-90 < a < 4.39999999999999997e-57

   1. Initial program 86.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(\frac{x}{y} + \frac{z}{z - a}\right) - \frac{t}{z - a}\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 99.9%

         \[\leadsto y \cdot \color{blue}{\left(\frac{x}{y} + \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\right)} \]

      2. div-sub 99.9%

         \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\frac{z - t}{z - a}}\right) \]

   5. Simplified 99.9%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} + \frac{z - t}{z - a}\right)} \]

   6. Taylor expanded in x around 0 95.1%

      \[\leadsto y \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{t}{z - a}\right)} \]
   7. Step-by-step derivation

      1. div-sub 95.1%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{z - a}} \]

   8. Simplified 95.1%

      \[\leadsto y \cdot \color{blue}{\frac{z - t}{z - a}} \]

   if 4.39999999999999997e-57 < a

   1. Initial program 74.0%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 74.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. inv-pow 74.1%

         \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]

   4. Applied egg-rr 74.1%

      \[\leadsto x + \color{blue}{{\left(\frac{z - a}{y \cdot \left(z - t\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 74.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}} \]

      2. associate-/r* 99.8%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{z - a}{y}}{z - t}}} \]

   6. Simplified 99.8%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{z - a}{y}}{z - t}}} \]

   7. Taylor expanded in t around 0 65.3%

      \[\leadsto \color{blue}{x + \frac{y \cdot z}{z - a}} \]
   8. Step-by-step derivation

      1. +-commutative 65.3%

         \[\leadsto \color{blue}{\frac{y \cdot z}{z - a} + x} \]

      2. associate-/l* 84.6%

         \[\leadsto \color{blue}{y \cdot \frac{z}{z - a}} + x \]

   9. Simplified 84.6%

      \[\leadsto \color{blue}{y \cdot \frac{z}{z - a} + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+81}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-41} \lor \neg \left(z \leq 1.35 \cdot 10^{+25}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.5e-41) (not (<= z 1.35e+25))) (+ y x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.5e-41) || !(z <= 1.35e+25)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.5d-41)) .or. (.not. (z <= 1.35d+25))) then
        tmp = y + x
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.5e-41) || !(z <= 1.35e+25)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.5e-41) or not (z <= 1.35e+25):
		tmp = y + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.5e-41) || !(z <= 1.35e+25))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.5e-41) || ~((z <= 1.35e+25)))
		tmp = y + x;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.5e-41], N[Not[LessEqual[z, 1.35e+25]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000022e-41 or 1.35e25 < z

   1. Initial program 73.6%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 76.3%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 76.3%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 76.3%

      \[\leadsto \color{blue}{y + x} \]

   if -5.50000000000000022e-41 < z < 1.35e25

   1. Initial program 96.0%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 71.5%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-41} \lor \neg \left(z \leq 1.35 \cdot 10^{+25}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-39} \lor \neg \left(z \leq 54000\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.2e-39) (not (<= z 54000.0))) (+ y x) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e-39) || !(z <= 54000.0)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.2d-39)) .or. (.not. (z <= 54000.0d0))) then
        tmp = y + x
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e-39) || !(z <= 54000.0)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.2e-39) or not (z <= 54000.0):
		tmp = y + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.2e-39) || !(z <= 54000.0))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.2e-39) || ~((z <= 54000.0)))
		tmp = y + x;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.2e-39], N[Not[LessEqual[z, 54000.0]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.20000000000000008e-39 or 54000 < z

   1. Initial program 74.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 75.9%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 75.9%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 75.9%

      \[\leadsto \color{blue}{y + x} \]

   if -1.20000000000000008e-39 < z < 54000

   1. Initial program 96.6%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 71.8%

      \[\leadsto \color{blue}{x + \frac{t \cdot y}{a}} \]
   4. Step-by-step derivation

      1. +-commutative 71.8%

         \[\leadsto \color{blue}{\frac{t \cdot y}{a} + x} \]

      2. associate-/l* 72.3%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} + x \]

   5. Simplified 72.3%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a} + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-39} \lor \neg \left(z \leq 54000\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 61.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+246} \lor \neg \left(t \leq 2.15 \cdot 10^{+226}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5e+246) (not (<= t 2.15e+226))) (* t (/ y a)) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5e+246) || !(t <= 2.15e+226)) {
		tmp = t * (y / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-5d+246)) .or. (.not. (t <= 2.15d+226))) then
        tmp = t * (y / a)
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5e+246) || !(t <= 2.15e+226)) {
		tmp = t * (y / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5e+246) or not (t <= 2.15e+226):
		tmp = t * (y / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5e+246) || !(t <= 2.15e+226))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5e+246) || ~((t <= 2.15e+226)))
		tmp = t * (y / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5e+246], N[Not[LessEqual[t, 2.15e+226]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.99999999999999976e246 or 2.14999999999999994e226 < t

   1. Initial program 82.0%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 67.1%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{z - a}} \]

   4. Taylor expanded in z around 0 56.4%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 63.6%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   6. Simplified 63.6%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   if -4.99999999999999976e246 < t < 2.14999999999999994e226

   1. Initial program 83.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 66.1%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 66.1%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 66.1%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+246} \lor \neg \left(t \leq 2.15 \cdot 10^{+226}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;t \leq 10^{+225}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.32e+185)
   (* y (/ t (- z)))
   (if (<= t 1e+225) (+ y x) (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.32e+185) {
		tmp = y * (t / -z);
	} else if (t <= 1e+225) {
		tmp = y + x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.32d+185)) then
        tmp = y * (t / -z)
    else if (t <= 1d+225) then
        tmp = y + x
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.32e+185) {
		tmp = y * (t / -z);
	} else if (t <= 1e+225) {
		tmp = y + x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.32e+185:
		tmp = y * (t / -z)
	elif t <= 1e+225:
		tmp = y + x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.32e+185)
		tmp = Float64(y * Float64(t / Float64(-z)));
	elseif (t <= 1e+225)
		tmp = Float64(y + x);
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.32e+185)
		tmp = y * (t / -z);
	elseif (t <= 1e+225)
		tmp = y + x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.32e+185], N[(y * N[(t / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+225], N[(y + x), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3199999999999999e185

   1. Initial program 83.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 86.4%

      \[\leadsto \color{blue}{y \cdot \left(\left(\frac{x}{y} + \frac{z}{z - a}\right) - \frac{t}{z - a}\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 86.4%

         \[\leadsto y \cdot \color{blue}{\left(\frac{x}{y} + \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\right)} \]

      2. div-sub 86.4%

         \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\frac{z - t}{z - a}}\right) \]

   5. Simplified 86.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} + \frac{z - t}{z - a}\right)} \]

   6. Taylor expanded in t around inf 72.1%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \frac{t}{z - a}\right)} \]
   7. Step-by-step derivation

      1. associate-*r/ 72.1%

         \[\leadsto y \cdot \color{blue}{\frac{-1 \cdot t}{z - a}} \]

      2. mul-1-neg 72.1%

         \[\leadsto y \cdot \frac{\color{blue}{-t}}{z - a} \]

   8. Simplified 72.1%

      \[\leadsto y \cdot \color{blue}{\frac{-t}{z - a}} \]

   9. Taylor expanded in z around inf 55.1%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \frac{t}{z}\right)} \]
   10. Step-by-step derivation

       1. associate-*r/ 55.1%

          \[\leadsto y \cdot \color{blue}{\frac{-1 \cdot t}{z}} \]

       2. mul-1-neg 55.1%

          \[\leadsto y \cdot \frac{\color{blue}{-t}}{z} \]

   11. Simplified 55.1%

       \[\leadsto y \cdot \color{blue}{\frac{-t}{z}} \]

   if -1.3199999999999999e185 < t < 9.99999999999999928e224

   1. Initial program 84.4%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 68.7%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 68.7%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 68.7%

      \[\leadsto \color{blue}{y + x} \]

   if 9.99999999999999928e224 < t

   1. Initial program 76.6%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 58.5%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{z - a}} \]

   4. Taylor expanded in z around 0 45.6%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 57.2%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   6. Simplified 57.2%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;t \leq 10^{+225}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.041:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+139}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -0.041) y (if (<= y 4.8e+139) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -0.041) {
		tmp = y;
	} else if (y <= 4.8e+139) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-0.041d0)) then
        tmp = y
    else if (y <= 4.8d+139) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -0.041) {
		tmp = y;
	} else if (y <= 4.8e+139) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -0.041:
		tmp = y
	elif y <= 4.8e+139:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -0.041)
		tmp = y;
	elseif (y <= 4.8e+139)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -0.041)
		tmp = y;
	elseif (y <= 4.8e+139)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -0.041], y, If[LessEqual[y, 4.8e+139], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0410000000000000017 or 4.80000000000000016e139 < y

   1. Initial program 63.2%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 53.0%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{z - a}} \]

   4. Taylor expanded in z around inf 38.2%

      \[\leadsto \color{blue}{y} \]

   if -0.0410000000000000017 < y < 4.80000000000000016e139

   1. Initial program 95.7%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 65.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.041:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+139}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 61.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.65 \cdot 10^{+148}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 4.65e+148) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 4.65e+148) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= 4.65d+148) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 4.65e+148) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 4.65e+148:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 4.65e+148)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 4.65e+148)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 4.65e+148], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 4.64999999999999992e148

   1. Initial program 86.7%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 61.5%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 61.5%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 61.5%

      \[\leadsto \color{blue}{y + x} \]

   if 4.64999999999999992e148 < a

   1. Initial program 62.4%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.65 \cdot 10^{+148}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 49.9% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x;
}

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 83.7%

   \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 47.1%

   \[\leadsto \color{blue}{x} \]

4. Final simplification 47.1%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{z - a}{z - t}} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ y (/ (- z a) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (y / ((z - a) / (z - t)));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (y / ((z - a) / (z - t)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (y / ((z - a) / (z - t)));
}

Python

def code(x, y, z, t, a):
	return x + (y / ((z - a) / (z - t)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(y / Float64(Float64(z - a) / Float64(z - t))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (y / ((z - a) / (z - t)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (/ (* y (- z t)) (- z a))))